Curved surface generator

ABSTRACT

Apparatus for generating complex curved surfaces such as the epitrochoidal bores of rotary combustion engines, e.g., &#39;&#39;&#39;&#39;Wankel&#39;&#39;&#39;&#39; engines. A workpiece is, in effect, fixed to a first imaginary cylinder which is rolled about the inner circumference of a larger second cylinder. A cylindrical cutting tool is positioned to contact the workpiece along a predetermined machining line which is parallel to the axes of the two imaginary cylinders, the machining line also being fixed relative to the larger of the two cylinders and outside of its outer circumference. The relative movement of the tool and workpiece causes the machining line to generate an eiptrochoidal surface on the workpiece, and this generated surface is maintained theroretically exact by maintaining the axis for the cylindrical cutting surface of the tool in a plane passing through the machining line and through the line of instantaneous tangency between the two imaginary cylinders as the smaller cylinder rolls relatively about the inner circumference of the larger cylinder. This combination of complex relative movements is provided by a relatively simple machine format which includes a drive mechanism utilizing three separately driven rotating gear members. The two members which simulate the rotation of the &#39;&#39;&#39;&#39;imaginary&#39;&#39;&#39;&#39; generating gears are concentrically mounted and do not intermesh or otherwise run relatively around the circumferences of each other, and all three drive gears rotate about axes which remain substantially fixed relative to each other at all times during machine operation.

ilnited States Patent 1 Peelers en [451 Sept. 11,1973

l l CURVED SURFACE GENERATOR [75] Inventor: Harry Peder-sen, Rochester,NY.

[73] Assignee: The Gleason Works, Rochester,

[22] Filed: Sept. 15, 1971 [21] Appl. No.: 180,585

[52] US. Cl. 51/33 W, 51/105 R [51] Int. Cl B24b 7/04 [58] Field ofSearch 51/32, 33 W, 105 R, 51/105 EC, 165.77, 95 W11; 82/18 [56]References Cited UNITED STATES PATENTS 3,494,388 2/I970 Sanders et al.82/18 X 3,595,108 2/1971 Priscsak 82/18 3,693,297 9/1972 Cann 51/95 WI-lX 2,870,578 1/1959 Baler 5l/9O FOREIGN PATENTS OR APPLICATIONS 914,981l/l963 Great Britain 5l/95 R 1,117,569 6/1968 Great Britain 51/95 RPrimary Examiner-Donald G. Kelly Assistant Examinerl-loward N. GoldbergAttorneyMorton A. Polster [57] ABSTRACT Apparatus for generating complexcurved surfaces such as the epitrochoidal bores of rotary combustionengines, e.g., Wankel" engines. A workpiece is, in effect, fixed to afirst imaginary cylinder which is rolled about the inner circumferenceof a larger second cylinder. A cylindrical cutting tool is positioned tocontact the workpiece along a predetermined machining line which isparallel to the axes of the two imaginary cylinders, the machining linealso being fixed relative to the larger of the two cylinders and outsideof its outer circumference. The relative movement of the tool andworkpiece causes the machining line to generate an eiptrochoidal surfaceon the workpiece, and this generated surface is maintainedtheroretically exact by maintaining the axis for the cylindrical cuttingsurface of the tool in a plane passing through the machining line andthrough the line of instantaneous tangency between the two imaginarycylinders as the smaller cylinder rolls relatively about the innercircumference of the larger cylinder. This combination of complexrelative movements is provided by a relatively simple machine formatwhich includes a drive mechanism utilizing three separately drivenrotating gear members. The two members which simulate the rotation ofthe imaginary generating gears are concentrically mounted and do notintermesh or otherwise run relatively around the circumferences of eachother, and all three drive gears rotate about axes which remainsubstantially fixed relative to each other at all times'during machineoperatron.

27 Claims, 10 Drawing Figures PATENTEI] SEN I I975 man or 5 HARRYPEDEESE/V INVENTOR.

PATENTED SEN I I975 SHEEI 5 [IF 6 PATENTED SE?! 1 I975 SHEET 8 BF 6CURVED SURFACE GENERATOR The invention herein relates to apparatus forgenerating curved surfaces, and more particularly to the generation ofsuch complex shapes as the epitrochoidal bores of rotary combustionengines.

BACKGROUND OF THE INVENTION While the invention is generally applicableto the machining'of all types of curved surfaces, it will be describedwith most particularity from the standpoint of machining bores forrotary combustion engines, e.g., Wankel engines. While this new form ofinternal combustion engine has not as yet received exceptionallywidespread usage, it is quite well known and seems to be gaining rapidlyin popularity, primarily because of its significant advantages over moreconventional internal combustion engines in relation to the part andweight reductions which can be realized.

As is well known, such rotary combustion engines utilize three-sidedrotary pistons which revolve about an eccentrically orbiting axis, andthe bore of the cylinder in which these pistons ride has anepitrochoidal shape.

The machining of epitrochoidal-bores for rotary combustion engines haspresented a major problem in that this shape is neither circular norelliptical and, therefore, is not readily amenable to machining bystandard milling, shaping, and grinding apparatus. In general, mostpresent methods of machining such epitrochoidal bores involve tracingthe desired tool motion from suitable cam shapes, However, such tracingsystems are far from satisfactory, particularly when extreme accuracy isrequired in such operations as final grinding.

One of the problems with such prior art tracing systems arises from thefact that the surface being traced is neither circular or rectilinearand, therefore, lines traced parallel to the cam shape will notreproduce the shape of the cam. That is, it is geometrically axiom aticthat when tracing a line parallel to a given geometric shape, a figuregeometrically similar to the original shape will be reproduced by suchparallel lines only if the original shape is either circular orrectilinear. Lines drawn parallel to any non-circular andnon-rectilinear shapes do not produce a figure similar to the figurebeing traced. Therefore, it can be appreciated that, as grinding wheelswear down in such prior art systems, the surface of the grinding wheelno longer traces the original shape but rather traces aline parallel tothe original shape and, since epitrochoids are neither circular norrectilinear, the resulting form produced by the worn grinding wheel isno longer geometrically similar to the original cam shape. One methodused by prior art systems to overcome these problems comprises usingcamfollowers having diameters which vary directly as the diameter of thegrinding wheels being used so that, as the latter become more and moreworn by repeated dressing, smaller and smaller cam followers are used totrace the cam.

Further, even when operating properly, many such prior art tracingsystems do not produce theoretically perfect surfaces, since the cuttingsurface of the machining tool is not maintained theoretically tangent tothe surface being machined at all times. Since all cutting tools are, bydefinition, wider than a geometric line," any lack of instantaneoustangency at the moment of cutting necessarily results in a deviationfrom a theoretically perfect surface.

Many prior art patents disclose apparatus for machining epitrochoidalsurfaces by generation, as distinguished from tracing," and thegenerating kinematics of all of these prior art machines are based uponone or the other of two geometric definitions of an epitrochoid. Thefirst defines an epitrochoid as the locus of a point fixed within afirst circle which rolls about the outer circumference of a largersecond circle.

in the second geometric definition, an epitrochoid is the locus of apoint fixed in relation to, and outside the circumference of, a firstcircle as the inner circumference of that first circle is rolled aroundthe outer circumference of a smaller second circle. While these knowngenerating devices do not suffer from the many problems referred toabove which plague tracing-type apparatus, they are all extremelycomplex mechanically in relation to both basic generating kinematics andto the means utilized for maintaining theoretical tangency between thecutting surface of the tool and the surface being generated.

Regardless of the geometric definition upon which epitrochoidalgeneration is based, most known prior art generators utilize drivetrains including actually intermeshed gear wheels which are equivalentin effective diameters to theoretical circles required by the geometricdefinitions referred to above, and in most cases such generating gearsliterally roll relatively about the outer or inner circumferences ofeach other. To state this in a different way, these known prior artgenerators are designed to use the same size gears for generation as areused in the engine to drive the rotor relative to the bore, and thisuniversally prevalent prior art machine format has severaldisadvantages. First of all, such actually sized gearing is relativelysmalland, as such, small variations in angular position, backlash, etc.,have fairly noticeable effects on the accuracy of the surface beinggenerated. In other words, with such gearing it is difficult to maintainthe very precise machining motions required for acceptable Wankel enginebores. Further, any changein engine bore size specifications oftenrequires that the basic drive of the machine be dismantled and acompletely different set of gearing be substituted, Finally, since suchintermeshed gearing is not and cannot be separately driven, such priorart generator is totally dedicated to the manufacture of one particularepitrochoidal shape.

The prior art also includes lathe-type machines for turning or boringnon-circular trochoidal shapes (e.g., U.S. Pat. Nos. 3,494,388 and3,595,108), and someof these machines do not utilize intermeshinggenerating gears which literally roll about each other. However, whilesuch machines are capable of forming epitrochoidal surfaces, they aredesigned to use single-point type cutting tools and cannot be used forprecision work with high-speed cylindrical cutting tools.

As noted above, precision generation requires that the cutting surfaceof the machining tool be maintained at all times theoretically tangentto the surface being generated. To achieve this necessary tangency, someprior art generators, such as that disclosed in British Patent No.914,981, superimpose further complex motions on the basic generatingmotion, while other prior art machines (e.g., U. S. Pat. No. 2,870,578)utilize intricate combinations of cranks, slides, slip joints, etc., toconstruct a mechanical equivalent of the theoretical geometricperpendicular. That is, as explained in greater detail below, it isknown that the perpendicular to any point on the surface of anepitrochoid passes through the instantaneous point of tangency betweenthe generating circles at the instant that point is generated, and thoseprior art machines which try to achieve such tangency either move theworkpiece or the cutting tool by means of a mechanism including onemember positioned at all times in actual physical alignment with theinstantaneous mesh point between the generating gears. Needless to say,in addition to being complex and expensive, such prior art machinery ismechanically congested and therefore, difficult to support and maintainfor accurate operation.

SUMMARY OF THE INVENTION The invention herein comprises a remarkablysimplified machine format for generating epitrochoidal shapes. it isbased upon generating kinematics related to the second geometricdefinition of an epitrochoid: the workpiece is effectively fixed to afirst imaginary cylinder which is then rolled relatively about the innercircumference of a second imaginary cylinder. The tool is positioned sothat its cylindrical cutting surface contacts the workpiece along amachining line which is parallel to the axes of the two imaginarycylinders, the machining line being fixed relative to the larger of thetwo cylinders and outside of its outer circumference. The relativemovement of the tool and workpiece cause the machining line to generatean epitrochoidal surface on the workpiece, and this generated surface ismain tained theoretically exact by maintaining the axisfor thecylindrical cutting surface of the tool in a plane passing through themachining line and through the line of instantaneous tangency betweenthe two imaginary cylinders as the smaller cylinder rolls relativelyabout the inner circumference of the larger cylinder.

It will be noted that the generating cylinders are referred to asimaginary because the invention herein, as different from prior artgenerators, does not use generating gears which duplicate either thetheoretical geometric generating circles or the actual gearing used inthe engine. Quite the contrary, the subject invention utilizes a machineformat in which the generating drive is no longer dependent upon theheretofore direct interconnection between the means for rotating thework table and they means for-orbiting the axis about which the worktable rotates.

In the preferred embodiment disclosed herein generation is accomplishedas follows: a first drive gear rotates a crank member which carries,in'an eccentric bearing, the axisof rotation of the work table. A seconddrive gear rotates the work table. This second drive gear does notintermesh with the first drive gear, i.e., one generating gear does notrun around the inner or outercircumference of the other. In fact, thesetwo drive gears are concentrically mounted and, in effect, areseparately driven but in a timed relationship such that their relativerotations simulate the rotations which would occur were the work tablefixed to a first imaginary gear which intermeshed with and run aroundthe inner'circumference of a larger second imaginary gear. Because thegenerating drive gears of the invention do not intermesh with eachother, there are no theoretical size limitations for these first andsecond generating drives, and they. can be built with as large acircumference as is deemed necessary to achieve the accuracy desired,i.e., large enough so that normallyexperienced elasticity in the drivetrain will not result in unacceptable movement variations in the worktable relative to the cutting tool, a problem which, as noted above,prevented the successful operation of prior art epitrochoidalgenerators.

Further, the eccentricity of the bearing which is carried by the crankmember and supports the axis of the work table, is adjustable and, moreimportantly, the adjustment of this bearing does not affect thegenerating drive. Thus, as distinguished from the operation of prior artgenerators, this feature makes it possible to alter the size of theepitrochoidal surface which is being generated without requiring anychange of the generating drive gears.

As just noted above, the separately driven first and second drive gearsare concentrically mounted and, since the work table rotates about anaxis eccentric to the common axis of these drive gears, an Oldhamcoupling is used to provide driving engagement between the second drivegear and the work table.

As to the tool-holding portion of the generator, the invention utilizesextremely simple apparatus to assure that the cutting surface of thetool remains tangent at all times to the surface of the desiredgenerated shape. As mentioned above, at any instant during thetheoretical geometric generation of an e'pitrochoid, a line drawnbetween the generating point and the instantaneous point of tangencybetween the generating circles will be perpendicular to the surfacebeing generated. Again, since there are no actual interrneshinggenerating gears in the invention herein, the plane which theoreticallypasses between'the machining line and the instantaneous mesh point ofthe imaginary generating cylinders, is also imaginary. The actual toolsupport mechanism merely comprises a lever arm, pivoted at the machiningline, and driven by a crank arm rotated by a third drive gear so thatthe movement of the lever arm simulates the theoretical movement of theimaginary plane. In the preferred embodiment, the crank arm driving thetool-holding lever arm is positioned remote from the work-holding tablefurther reducing machine congestion and making possible greaterstiffness and easier'maintenance.

While only the presently preferred form of the apparatus is disclosed indetail, three different possible machine configurations are discussed.

In describing the invention with greater particularity, reference willbe; made to the accompanying drawings in which like reference charactersdesignate corresponding or theoretically similar partsthroughout theseveral views and in which:

FIGS. 1A and 1B illustrate, respectively, the two geometric definitionsfor epitrochoids;

FIGS. 2A, 2B and 2C show, respectively, three different possiblekinematic machine configurations for the novel curved surface generatordisclosed herein;

FIGS. 3A and 3B are schematic representations of two possible variationsof apparatus for maintaining the cutting surface of the tooltheoretically tangent to the surface being generated by the preferredkinematic arrangement illustrated in FIG. 2C;

FIG. 4 is a partially schematic and cross-sectional side elevation viewof a preferred form of apparatus for the invention disclosed herein;

FIG. 5 is a schematic plan view of the work table portion of theapparatus disclosed in FIG. 4; and

FIG. 6 is a schematic plan view of the tool-holding portion of theapparatus disclosed in FIG. 4.

GEOMETRIC BASIS FOR GENERATION Referring now to FIGS. 1A and 1B, the twogeometric methods for defining epitrochoids are shown. In FIG. 1A, theepitrochoidal shape 10 is shown in dashed lines. If a smaller circle 12is rolled about the outer circumference of a larger circle 14, the locusof center C of the smaller circle is a third circle 16 having a radiusequal to the sum of the radii of circles 12 and 14. However, the locusof any point P within smaller circle 12 is a curved line 10 called anepitrochoid.

It is possible, geometrically, to define an epitrochoidal curve inanother manner, and this is shown in FIG. 1B. Smaller circle 12' isfixed within larger circle 14'. If the inner circumference of the largercircle is rolled about the outer circumference of the smaller innercircle, the locus of the center C of the larger circle is a third circle16' smaller than the other two circles, namely, the radius of the thirdcircle being equivalent to the difference between the radii of circle14' and 12'. The locus of a point P fixed relative to and outside oflarger circle 14' is an epitrochoid 10. Special attention is called tothe geometric definition illustrated in FIG. 1B, since it will serve tofacilitate understanding of the novel apparatus disclosed herein and tosubstantiate the effectiveness of the method utilized by the inventionfor generating theoretically perfect epitrochoidal surfaces.

THREE KINEMATIC VARIATIONS OF THE GENERATION METHOD FIGS. 2A, 2B and 2Cillustrate three difi'erent theoretical systems of machine kinematics,any one of which may be utilized by apparatus according to the inventionherein to generate epitrochoidal surfaces. In each of these machineembodiments, a workpiece W is fixed to a first cylinder 22 positioned sothat its outer circumference is tangential to the inner circumference ofa second larger cylinder 24. The two cylinders, which have respectiveaxes 23 and 25 connected by a crank 26, are adaptedto permit relativemovement between them without slippage, e.g.,-the larger cylinder maycomprise an internal gear while the smaller cylinder may comprise anexternal gear having mating teeth. Also, in each of the three differentembodiments a tool T is positioned so that its cutting surface passesthrough a machining line M which is parallel to axes 23 and 25 and fixedin relation to larger cylinder 24 outside of the latters outercircumference. For purposes of this disclosure, it will be assumed thattool T is a grinding wheel. However, it should be noted that tool T maybe any type of tool having a cylindrical cutting surface, for instance,a milling cutter or a shaping tool may be used as well as a cylindricalgrinding wheel.

In each of the three machine embodiments shown in FIGS. 2A, 2B and 2C,the axis 27 of the cutting surface of tool T is maintained at all timesin an imaginary plane containing machining line M and the instantaneousline of tangency between cylinders 22 and 24 (this instantaneousimaginary plane being represented in the drawings by the lines N, N,,,N,, and N By providing a relative rolling of smaller cylinder 22 aboutthe inner circumference of larger cylinder 24, and by fixing a machiningline M relative to larger cylinder 24, as explained above, it can beseen that the locus of machining line M will generate an epitrochoidalsurface in the same manner as line 10' was traced geometrically in FIG.18. It can also be shown geometrically that imaginary plane N, definedin the manner just described above, will always be perpendicular to thegenerated surface 30. Therefore, since tool T has a cylindrical cuttingsurface, as long as axis 27 of this cutting surface remains in imaginaryplane N, tool T willalways theoretically be cutting workpiece W alongmachining line M with its cutting surface tangent to generated surface30.

Thus, it will be understood that the basic geometric method underlyingthe three schematic machine embodiments shown in FIGS. 2A, 2B and 2Cprovides a means for machining true epitrochoidal surfaces on workpieceW. In this regard, it should be noted that tool T does not necessarilyhave to be positioned to machine an internal bore in workpiece W butcould also be used to machine curved outer surfaces as well merely bypositioning tool T on the outside of machining line M but still, ofcourse, retaining axis 27 at all times in imaginary plane N.

The three machine embodiments shown in FIGS. 2A, 2B and 2C all difi'erkinematically, even though they share the similarities of the methoddiscussed above, e.g., workpiece W always being fixed to inner cylinder22, machining line M always being fixed relative to and outside oflarger cylinder 24, etc. In the embodiment shown in FIG. 2A, workpiece Wand smaller cylinder 22 are fixed, and the relative rolling motion isobtained by orbiting larger cylinder 24 about the outer circumference ofthe smaller inner cylinder. In this embodiment, crank 26 is rotatedabout axis 23 of cylinder 22 causing axis 25 of larger cylinder 24 toorbit in the direction of arrow 32. At the same time, larger cylinder 24is rotated about its axis 25 in the direction of arrow 34. Thus, whileworkpiece W remains fixed, the cutting surface of tool T revolves'andorbits with larger cylin der 24 to generate surface 30. Assuming thatthe ratio of the effective diameters of the two cylinders is 3:2, crank26 must turn two complete revolutions to cause machining line M togenerate the complete surface 30. This general machine motion isillustrated by showing a second position for the moving machine parts indotted lines. Thus, when crank 26 moves to the position indicated byreference numeral 26a it orbits center 25 of larger cylinder 24 to theposition indicated by reference numeral 25a, the original point oftangency 36 between the two cylinders being rolled around to point 36a.At the same time, tool T is moved to position T,, thereby maintainingits cylindrical cutting surface on the machining line (which has movedto M.) and retaining its same relative position to larger cylinder 24.However, special attention is called to the fact that during thismovement of tool T its axis 27 has not remained fixed relative to largercylinder 24 but rather has moved relatively (to the left in the drawing)to remain on the new instantaneous imaginary plane N, which no longerpasses through axis 25 (now moved to 25a) but instead passes through thenew machining line M. and the instantaneous point of tangency 360. Whilethe general machine structure shown in FIG. 2A allows the workpiece W toremain in a fixed location, it is considered the least desirable of thethree disclosed kinematic embodiments.

In the embodiment disclosed in FIG. 2B, crank member 26 remains fixed,i.e., both small cylinder 22 and 'dles. I

1 large cylinder 24 revolve about their respective axes 23 and'25 whichremain fixed in space. Since workpiece W is fixed to cylinder 22, itrevolves with cylinder 22, as indicated in-the drawing by the dashedlines and ref erence letter W,,. Again assuming a ratio of efl'ectivecylinder diameters of 2:3, when workpiece W rotates with cylinder 22 tothe position indicated by the refer-' ence letters W,,, large cylinder24 rotates in the same direction, but only two-thirds as far, moving themachining line with it to the new position indicated by the I referenceletters M Tool T follows this movement to imaginary plane established atany given instant in time by both the machining point and the point oftangency between the two cylinders. (In this case, of course, the

' point of tangency between the twocylinders remains fixed while themachining line moves with cylinder 24.)

While this particular embodiment is-the simplest-kinematically, it haspractical disadvantages relating to machine rigidity and to thesupplying of power to. the spin- FIG. 2C schematically illustrates thegeneral kinematic format of a preferred embodiment of apparatus forcarrying out the invention disclosed herein. According to this thirdvariation, the larger cylinder 24 remains fixed, while crank 26 rotatesto orbit axis 23 of smaller cylinder 22 in the direction of arrow 38. Atthe same time, smaller cylinder 22 rotates about'its axis 23 in thedirectionof arrow 40. Therefore, the workpiece both rotates and orbitswith smaller cylinder 22, while machining line M remains fixed. Theserelative motions can be visualized with the help of the dotted lineelements in FIG. 2C which indicate that when crank 26 moves to theposition indicated'by reference numeral 26c, smaller cylinder 22 rotatesand orbits to the position indicated by reference numeral 22c, carryingthe workpiece to the position indicated bythe reference letters W andcausing the instantaneous line of tandoes not utilize any generatingdrive gears which roll about the circumferences of each other, it canbcsaid,

that cylinders 22 and 24 may be considered imaginary in the same sensethat the blades of a face mill cutter used in a gear generating machinecan be said to 7 represent a single toothof an imaginary gear matingwith the gear being cut.

OSCILLATING TOOL SUPPORT VARIATlONS Therefore, in both FIG. 3A and FIG.38 it is assumed that workpiece W has been rotated and orbited in thesame manner as shown in FIG. 2C and that tool T has moved similarly,oscillating the axis of its cutting surface from an original positionindicated by reference numeral 27 to a new position indicated byreference numeral 27c.

In FIG. 3A tool T is suitably mounted to an oscillating support 42 whichis itself pivoted at a point on machining line M. A slot 44 in support42 receives pin 46 which is mounted to one end of a crank arm 48, theopposite end of the crank arm being pivoted about an axis coincidentwith axis 25 of large cylinder 24 (see FIG.

2C). The effective length of crank arm 48 is equivalent to the radiusofimaginary cylinder 24, and the crank arm is rotated about axis 25 inthe direction of arrow 50 at a rate which causesthe center of pin 46 toremain 1 at alltimes coincident with the instantaneous'line of tangency36 between imaginary cylinders 22 and In this manner, tool axis 27remains at all times on the imaginary plane containing machining line Mand the" instantaneous line of tangency between the cylinders. This isillustrated in FIG. 3A by showing crank arm 48 rotated from its originalposition to a dotted line position corresponding to an appropriatemovement to gency between the cylinders to move from point 36 to Whilemachining line M remains stationary embodiment, attention is once againcalled to the fact that tool T does not remain stationary. In-order to imaintain theoretical tangency between the cylindrical cutting surface ofthe tool and generated surface 30,

i tool axis 27 oscillates about machining-pointM so that it remains onthe imaginary plane containing both machining point M and theinstantaneous line of tangency between the cylinders. -(At the instantshown in dotted lines, the tool axis is at the point indicated byreference numeral 27c.)

isbased upon the fact that any mechanismwhich kine-' maticallyreproduces the motion represented by the relative movements of cylinders22and 24 and of crank 26--will produce the desired generation.Therefore,

since the novel generating apparatus of the invention in this paratus isillustrated in FIG. 3B which, as just noted above, assumes the samerelative movement of workpiece W and tool T as was illustrated in FIGS.2C and 3A. In this embodiment, tool T is similarly appropriately mountedto an oscillating support member 52 which is similarly pivoted at apoint on machining line M. Support 52 also'includes a slot 54 whichreceives a pin 56 of a crank arm 58. However, in this case a secondcrank arm 58 (as distinguished from first crank arm 26 shown in FIG. 20)is arranged for rotation about an axis 60 which, while parallel to bothmachining line M and fixed axis 25 of larger cylinder 24 (see FIG. 2C),is relatively remote from the other machine elements. The radius ofcrank ann 58 is selected so that rotation of the crank will cause thecenter line of oscillating tool support 52 to remain at all times in theplane N in the manner and for the reasons described above. Again, therelative motion of this tool supporting apparatus is indicated by dottedlines to show the relative position positions as illustrated in FIGS. 2Cand'SA. It should be noted that crank arm 58 rotates in the samedirection as crank arm 48 in the embodiment illustrated in FIG. 3A, andin also the same direction as crank 26 as shown in FIG. 2C. However,while it rotates at the same rate as the instantaneous line of tangencyof the two cylinders (indicated for two relative cylinder positions bypoints 36 and 36c in FIG. 2C), pin 56 is 180 out of phase with theinstantaneous line of tangency.

As distinguished from the embodiment shown in FIG. 3A, in which theoscillating tool support is driven by a crank having its axis coincidentwith first crank axis 25, in the preferred variation shown in FIG. 33second crank axis 60 is positioned remote from first crank axis 25 andthe work supporting apparatus, thus avoiding congestion and making iteasier to provide greater rigidity and easier maintenance for the tooloscillating mechanism.

PREFERRED APPARATUS As explained above, apparatus for carrying out theinvention does not actually utilize large and small cylinders. In thepreferred embodiment of apparatus disclosed in FIGS. 4-6, awork-supporting means (to which workpiece W is mounted) is carried by acrank member in a bearing which is adjustable eccentric to a first axisabout which the crank rotates. The worksupporting means is itselfrotated about a second axis which passes through the adjustable bearingand is parallel to the first axis of the crank member. In this marinerthe work-supporting means is rotated about the second axis while thatsecond axis orbits about the first axis, the rates of rotation andorbiting being predetermined in accordance with the speed at which afirst imaginary cylinder of suitable diameter would have to roll aboutthe interior of a second larger imaginary cylinder in relation to afixed point outside the larger -cylinder in order to produce theepitrochoidal shape desired.

Work Table Referring first to FIGS. 4 and 5, workpiece W is securelymounted to the top of a work table 62 which, in turn, is affixed to alarge shaft 64 journaled for rotation within a bearing member 66 aboutaxis 23 which repre sents the axis of inner imaginary cylinder 22 inFIG. 2C. A drum 68 is journaled for rotation within a slide 70 which, inturn, is adjustable by conventional means (not shown) along suitableways 69 formed ina machine frame 71. Drum 68 rotates about axis 25,efi'ectively representing crank 26 (of FIG. 2C) which rotates about theaxis of fixed largercylinder 24. Drum 68 has a generally rectangularbore 72 through which bearing member 66 is carried on slides 74. Theposition of bearing member 66 within bore 72 is adjusted to change thedistances between axes 23 and 25, bearing member 66 being suitablysecured to slides 74 by clamping means (not shown). Thus, it can be seenthat drum 68 acts as a crank means, serving as the kinematic equivalentof crank 26 of FIG. 2C, the rotation of drum 68 efi'ectively causingaxis 23 to orbit about axis 25. Also, since drum 68 moves with slide 70,adjustment of the latter varies the distance between axis 25 of thelarger imaginary cylinder and the machining line M to alter the size andthe proportions of the surface being generated. Drive Mechanism I Thedrive mechanism for the work table comprises a motor 76 and a drivetrain including spur gears 78 and 80 and telescoping shaft 82. Therotation of shaft 82 drives a first worm 84 and its associated firstworm wheel 86, the latter having a hub portion 88 suitably journaled inslide 70. Shaft 82 also drives a second worm-worm wheel combination 90and 92 through a second pair of spur gears 94, 96 and a shaft 98. (Note:portions of drum 68, worm 90, worm wheel 92, and shaft 98 have beenremoved from FIG. 4 to facilitate illustration of the machine parts.)Second worm wheel 92 is suitably fixed to drum 68 causing the rotationof the latter, while the purpose of worm wheel 86 is to provide thenecessary rotation of shaft 64 and work table 62 about axis 23. It willbe appreciated that selection of gear ratios for this drive mechanismcan be made to simulate different relative diameters for the imaginarycylinders even though the two generating drive gears (worm wheels 86 and92) do not actually intermesh and even though their actual diameters arenot in the ratio of 3:2 (the ratio required of the imaginary cylindersin order to generate a two-lobed epitrochoid such as is utilized as thebore of a Wankel engine).

Since first worm wheel 86 is fixed in slide while work table 62 andshaft 64 orbit eccentrically about axis 25, the necessary drivingconnection between these members is provided by a conventional Oldhamcoupling, namely, by a disc HBO-having keys 102 and 104 formed on itsopposite sides and at angles to each other. Keys 102 and 104 cooperatewith respective keyways 106 and 108 formed in the respective lower andupper surfaces of two flanges 110, 1 l2 suitably fixed, respectively, toshaft 64 and worm wheel 86. This coupling arrangement causes shaft 64 torotate in constant velocity ratio with worm wheel 86 regardless of therelative eccentric displacement between axes 23 and 25. It will beappreciated that this mechanical arrangement makes it possible to 'varythe size of the epitrochoidal surface being generated without in any wayhaving to change the generating described above.

ToolSupport Referring now to FIGS. 4 and 6, tool T is mounted toapparatus generally supported by an annular section 113 of frame 71formed between two upstanding column members 114. The oscillating toolsupport 52 includes two major movable elements, namely, (1 oscillating.support 116 shaped like a frying-pan and having an annular portion 1 l8rotatably mounted on annular section 113 of the frame-for angularmovement about the machining line M, and (2) a slide 120 supported onball bearing elements 122 to ride on parallel ways 124 formed on theedges of a generally rectangular cavity 126 formed in the center ofannular portion 118 of oscillating support 116.

For oscillating the movable tool support elements, a shaft 128 driven bymotor 76 through spur gears 78 and so, Shea s2, worm 130 and worm wheel132, carries crank arm 58 for rotation about axis 60. Pin 56 at theouter end of crank arm 58 is received in slot 54 formed in oscillatingsupport 116 (in the handle" of the frying-pan). As crank 58 is drivenaround axis 60, its pin 56 causes support 116 to oscillate about line M(in the manner explained above and also shown in FIG. 38).

Tool T is mounted to a spindle 134 held in a quill 136 which, in turn,is supported for vertical movement in slide 120. Mounted to quill 136.is a motor 138 which drives spindle 134 by means of a belt 140 andappropriate pulleys.

drive mechanism just in order to improve surface finish, tool T isoscillated along its axis 27 by means of a motor 142 which is alsomounted on quill 136. Motor 142 carries a face cam 144 which rides overa roller fixed to slide 120, the rotation of face cam 144 acting againstroller 146 to raise and lower quill 136 relative to slide 120.

As mentioned above, while the method disclosed herein can be practicedwith any cylindrical machining tool, the preferred form of apparatusshown in FIGS. 4-6 uses a cylindrical grinding wheel. This grindingwheel is dressed by a diamond wheel 148 driven by a small dressing motor150 which can be adjusted and fixed in various positions by a slidemounting 151 on the bottom of annular portion 118 of oscillating toolsupport 1 16. Dressing is accomplished as the surface of tool T is movedvertically past tool-shaping edge 152 of diamond wheel 148 by theraising of quill 136 relative to slide 120 by a hydraulicpiston-cylinder arrangement indicated schematically at 153.

As grinding wheel tool T wears down, it must also be fed horizontallyinto the tool-shaping edge 152 of diamond wheel 148. This isaccomplished by means of a motor 154 mounted on an outer upstandingflange 156 of annular portion 118 of oscillating support 116. Motor 154rotates an adjusting screw 158 which is received in a threaded portionof another upstanding flange 160 formed along the outer edge of slide120. Rotation of screw 158 by motor 154 causes slide 120 to move alongthe center, line of oscillating support 1 16. Since the rotation ofcrank 58 is designed to cause this center line to lie at all times inimaginary plane N, it is important to note that this tool wear adjustingmechanism permits axis 27 of tool T to remain properly aligned with theimaginary normal plane N. Therefore, regardless of the diameter of thecutting surface of tool T, the cutting surface of tool T always remainstheoretically tangent to the surface being generated on workpiece W. Asshown in FIG. 4, dressing motor 150 is adjusted in slide mounting 151 sothat the tool shaping edge 152 of diamond wheel 148 is exactly alignedwith the machining line M. However, it will be appreciated that theposition of tool shaping edge 152 relative to machining line M can bealtered in accordance with well-known practices. For instance, thoseskilled in machining arts will appreciate that, if tool T were withdrawndirectly upward from its machining position against the surface beinggenerated in workpiece W, scratching of the generated surface mightresult. Therefore, in practical operation, prior to vertical movement oftool T (under the control of piston-cylinder arrangement 153) to permitunloading of the workpiece and/or dressing of tool T, motor 154 may alsobe operated to withdraw the tool slightly away from the workpiece. Insuch event, the position of tool shaping edge 152 of dressing wheel 148would be adjusted accordingly to align with the slightly withdrawnposition of tool T. Also, as will be obvious to those skilled in theart, when an unfinished workpiece is initially loaded into the worktable, motor 154 is used to gradually feed tool T toward its finalposition, such gradual in-feed being necessary to avoid burning and toprevent excessive cutting loads on the tool. Of course, it will beappreciated that such in-feed could be as well accomplished by suitablesmall movements of slide 70 on ways 69, or column members 114 could bemade similarly movable on frame 71 to provide the desired relative feedmotion between tool T and workpiece W.-

It should also be understood that if the drive mechanism were run at aconstant speed, thereby imparting similarly constant speeds to rotateand orbit work table 62 in the manner explained above, the unusualcombined rotating and orbiting movement of workpiece W in relation totool T would cause workpiece W to pass through machining line M at rateswhich vary considerably depending upon the particular position of themachine elements in the generating cycle. Since there is often anoptimum rate of feed in machining operations, the invention hereinincludes a variable speed control means including a speed earn 162 fixedto shaft 128. While illustrated 'in a very schematic manner, it will beunderstood that a cam follower 164 drives the speed control lever 166 ofa rheostat device 168 which controls the circuit energizing motor 76. Itwill be appreciated that by appropriate shaping of cam 162 it ispossible to control the speed of motor 76 to maintain a constant feed ofworkpiece W to tool T.

Generation of Other Curved Surfaces While the invention herein has beendescribed primarily for its ability to generate epitrochoidal surfaces,it should be understood that other surfaces can be generated as well.For instance, if too] T is' positioned so that its cutting edge isparallel to, but no longer in exact alignment with, machining line M,the tool will no longer generate a true epitrochoid but rather willgenerate a surface parallel to an epitrochoid. This latter type ofsurface is often desired when manufacturing the bore of rotarycombustion engines because, while the ends of the rotors of such anengine do trace epitrochoidal surfaces, the bore of the engine must beenlarged to accommodate suitable seals which must necessarily extendbeyond the ends of the engine rotor. Therefore, the surface traced bythe seals is no longer truly epitrochoidal but is rather a surfaceparallel to a truly epitrochoidal surface. (since, as was noted above,an epitrochoid is neither circular nor rectilinear, a line parallel toit will trace some shape different from a true epitrochoid.)

Similarly, during any particular portion of the generating cycle, motor154 can be operated to rotate screw 158, thereby altering the positionof slide relative to the oscillating support member 116 and causing themachining surface of tool T to move away from or back into alignmentwithmachining line M. It'will be appreciated that any such change duringgeneration will alter the shape of the curved surface being generating.

lt'will also be understood that, by changing gear ratios in the drivemechanism, thesize of the imaginary cylinders can be varied to generateother variations of trochoidal surfaces. It should also be noted that inthe event bearing member 66 is moved on slide 74 of drum 68 to bringaxes 23, 25 into coincidence, tool T will generate a true cylindricalsurface. The method .and apparatus of the invention have been disclosedin a relatively schematic manner to facilitate understanding by thoseskilled in the art without the undesirable clutter of unnecessarilydetailed machine drawings, and it will be understood that suchobvious-but-omitted details can be readily supplied by personsknowledgeable in the fabrication of machine tools.

What is claimed is:

1. Apparatus for generating epitrochoidal and other curved surfaces on aworkpiece comprising:

frame means;

crank means mounted to said frame means for rotation about a crank axis;

adjustable bearing means carried by said crank means; work-supportmeans, for holding said workpiece, mounted for rotation about awork-support axis passing through said bearing means parallel to saidcrank axis for movement with said crank means about said crank axis, thedistance between said crank and work-support axes varying in accordancewith the adjustment of said bearing means;

tool-support means for holding a tool having a cylindrical cuttingsurface so that said cutting surface passes in proximity to apredetermined stationary machining line parallel to said crank axis,said toolsupport means being mounted for oscillation about atool-support axis which is coincident with said machining line, and

drive means for rotating said crank means and worksupport means and foroscillating said tool-support means, respectively, in timedrelationships.

2. Apparatus according to claim 1 wherein said drive means comprisesseparately driven first and second members rotatable about axes fixedrespective to each other and drivingly engaged respectively to saidworksupport means and said crank means.

3. Apparatus according to claim 2 wherein the axes of said first andsecond rotatable drive members are both coincident with said crank axis.

4. Apparatus according to claim 2 wherein the axes of said first andsecond rotatable drive members remain fixed relative to each other whenthe distance between said crank and work-support axes is varied byadjustment of said bearing means.

5. Apparatus according to claim 4 wherein Oldham coupling meansdrivingly engage said first rotating member and said work-support means.

6. The apparatus of claim 1 further comprising second adjusting meansfor varying the distance between said crank and tool-support axes.

7. The apparatus of claim 1 wherein said drive means rotates said crankmeans and work-support means, respectively, in opposite directions.

8. The apparatus of claim 1 wherein said tool-support means comprises asecond crank means rotatable about a second crank axis parallel to saidfirst crank axis.

9. The apparatus of claim 8-wherein the distance between said first'andsecond crank axes is greater than the distance between said first crankaxis and said work-support axis.

10. The apparatus of claim 8 wherein said drive means rotates said firstand second crank means at the same rate.

11. Apparatus of claim 1 wherein said drive means includes means forvarying the rate of rotation of said crank means and said work-supportmeans and the rate of oscillation of said tool-support means inaccordance with their relative positions.

12. In a machine for generating epitrochoidal and other curved surfaceson a workpiece, said machine having crank means mounted for rotationabout a first axis,

work-holding means mounted for movement with said crank means about saidfirst axis, said workholding means also being rotatable simultaneouslyabout a second axis offset from said first axis, and

tool-holding means for receiving a tool having an effectivelycylindrical cutting surface and positioning said cutting surface inproximity to a stationary machining line parallel to said first axis andlocated at a predetermined distance from said first axis, the axis ofsaid tool also being substantially parallel to said first axis, theimprovement comprising: movable support means for mounting saidtoolholding means, for oscillatory movement about a third axiscoincident with said machining line, and drive means for separatelyrotating, respectively, said crank means and said work-holding means,for timing said separately driven rotations in a relationshippredetermined to simulate the relative rotation of a first imaginarycylinder fixed to said work-holding means about the inner circumferenceof a larger second imaginary cylinder having an axis coincident withsaid first axis, the distance between said machining line and said firstaxis being greater than the radius of said second imaginary cylinder,and for oscillating said movable support means to maintain said toolaxis at all times so that it lies in an imaginary plane passing throughsaid machining line and through the instantaneous point of tangencybetween said imaginary cylinders.

13. A machine according to claim 12 wherein said drive means comprisesfirst and second drive members connected for movement, respectively,with said workholding means and said crank means, each member beingseparately driven and rotatable according to said predetermined timedrelationship about respective axes fixed in relation to each other.

14. A machine according to claim 13 wherein said first and second drivemembers rotate about axes coincident with said first axis.

15. A machine according to claim 12 wherein said crank means includesadjustable bearing means and said work-holding means is mounted so thatsaid second axis passes through said bearing means, the distance betweensaid first and second axes varying in accordance with the adjustment ofsaid bearing means.

16. A machine according to claim 15 wherein said drive means comprisestwo separately driven members connected for movement with said crankmeans and said work-holding means and rotatable about axes coincidentwith said first axis, the axes of said driven members remainingcoincident with said first axis regardless of the distance between saidfirst and second axes as determined by adjustment of said bearing means.

17. A machine according to claim 16 wherein Oldham coupling meansdrivingly engage one of said driven members and said work-holding means.

18. A machine according to claim 12 wherein said drive means comprisestwo separately driven cylindrical members connected for movement,respectively, with said crank means and said work-holding means, eachsaid cylindrical member being rotatable according to said predeterminedtimed relationship and each being larger in circumference than thelarger of said imaginary cylinders.

19. The machine according to claim 12 wherein said movable support meansis efiectively pivoted at said third axis, and wherein said machinesfurther comprises a second crank means operatively engaging said supportmeans and rotatable about a fourth axis, said drive means rotating bothsaid first and second crank means at the same speed.

20. The machine according to claim 19 wherein the distance between saidfourth axis and said first axis is greater than the distance betweensaid first axis and said machining line.

21. The machine according to claim 1 wherein said tool is a cylindricalgrinding wheel having a tool axis parallel to said machine line.

22. The machine according to claim 21 further comprising wheel dressingmeans movable relative to said grinding wheel for dressing the surfacethereof, said dressing means being positioned to contact the cuttingsurface of said grinding wheel along a predetermined dressing line whichis substantially parallel to said tool axis.

23. The machine according to claim 22 wherein said dressing line iscoincident with said machining line.

24. The machine according to claim 23 wherein the distance between saiddressing line and said crank axis is less than the distance between saidcrank axis and said machining line.

25. The machine according to claim 12 further comprising means formoving said tool axis along said imaginary plane relative to saidmachining line.

26. The machine according to claim 19 comprising further means carriedby said support means for moving said tool axis relative to saidmachining line along said imaginary plane.

27. Th machine according to claim 12 wherein said drive means rotatessaid crank means about said first axis in a first direction whilerotating said W01'kh0ldlhg means about the second axis in the oppositedirection. t t k

1. Apparatus for generating epitrochoidal and other curved surfaces on aworkpiece comprising: frame means; crank means mounted to said framemeans for rotation about a crank axis; adjustable bearing means carriedby said crank means; work-support means, for holding said workpiece,mounted for rotation about a work-support axis passing through saidbearing means parallel to said crank axis for movement with said crankmeans about said crank axis, the distance between said crank andwork-support axes varying in accordance with the adjustment of saidbearing means; tool-support means for holding a tool having acylindrical cutting surface so that said cutting surface passes inproximity to a predetermined stationary machining line parallel to saidcrank axis, said tool-support means being mounted for oscillation abouta tool-support axis which is coincident with said machining line, anddrive means for rotating said crank means and work-support means and foroscillating said tool-support means, respectively, in timedrelationships.
 2. Apparatus according to claim 1 wherein said drivemeans comprises separately driven first and second members rotatableabout axes fixed respective to each other and drivingly engagedrespectively to said work-support means and said crank means. 3.Apparatus according to claim 2 wherein the axes of said first and secondrotatable drive members are both coincident with said crank axis. 4.Apparatus according to claim 2 wherein the axes of said first and secondrotatable drive members remain fixed relative to each other when thedistance between said crank and work-support axes is varied byadjustment of said bearing means.
 5. Apparatus according to claim 4wherein Oldham coupling means drivingly engage said first rotatingmember and said work-support means.
 6. The apparatus of claim 1 furthercomprising second adjusting means for varying the distance between saidcrank and tool-support axes.
 7. The apparatus of claim 1 wherein saiddrive means rotates said crank means and work-support means,respectively, in opposite directions.
 8. The apparatus of claim 1wherein said tool-support means comprises a second crank means rotatableabout a second crank axis parallel to said first crank axis.
 9. Theapparatus of claim 8 wherein the distance between said first and secondcrank axes is greater than the distance between said first crank axisand said work-support axis.
 10. The apparatus of claim 8 wherein saiddrive means rotates said first and second crank means at the same rate.11. Apparatus of claim 1 wherein said drive means includes means forvarying the rate of rotation of said crank means and said work-supportmeans and the rate of oscillation of said tool-support means inaccordance with their relative positions.
 12. In a machine forgenerating epitrochoidal and other curved surfaces on a workpiece, saidmachine having crank means mounted for rotation about a first axis,work-holding means mounted for movement with said crank means about saidfirst axis, said work-holding means also being rotatable simultaneouslyabout a second axis offset from said first axis, and tool-holding meansfor receiving a tool having an effectively cylindrical cutting surfaceand positioning said cutting surface in proximity to a stationarymachining line parallel to said first axis and located at apredetermined distance from said first axis, the axis of said tool alsobeing substantially parallel to said first axis, the improvementcomprising: movable support means for mounting said tool-holding means,for oscillatory movement about a third axis coincident with saidmachining line, and drive means for separately rotating, respectively,said crank means and said work-holding means, foR timing said separatelydriven rotations in a relationship predetermined to simulate therelative rotation of a first imaginary cylinder fixed to saidwork-holding means about the inner circumference of a larger secondimaginary cylinder having an axis coincident with said first axis, thedistance between said machining line and said first axis being greaterthan the radius of said second imaginary cylinder, and for oscillatingsaid movable support means to maintain said tool axis at all times sothat it lies in an imaginary plane passing through said machining lineand through the instantaneous point of tangency between said imaginarycylinders.
 13. A machine according to claim 12 wherein said drive meanscomprises first and second drive members connected for movement,respectively, with said work-holding means and said crank means, eachmember being separately driven and rotatable according to saidpredetermined timed relationship about respective axes fixed in relationto each other.
 14. A machine according to claim 13 wherein said firstand second drive members rotate about axes coincident with said firstaxis.
 15. A machine according to claim 12 wherein said crank meansincludes adjustable bearing means and said work-holding means is mountedso that said second axis passes through said bearing means, the distancebetween said first and second axes varying in accordance with theadjustment of said bearing means.
 16. A machine according to claim 15wherein said drive means comprises two separately driven membersconnected for movement with said crank means and said work-holding meansand rotatable about axes coincident with said first axis, the axes ofsaid driven members remaining coincident with said first axis regardlessof the distance between said first and second axes as determined byadjustment of said bearing means.
 17. A machine according to claim 16wherein Oldham coupling means drivingly engage one of said drivenmembers and said work-holding means.
 18. A machine according to claim 12wherein said drive means comprises two separately driven cylindricalmembers connected for movement, respectively, with said crank means andsaid work-holding means, each said cylindrical member being rotatableaccording to said predetermined timed relationship and each being largerin circumference than the larger of said imaginary cylinders.
 19. Themachine according to claim 12 wherein said movable support means iseffectively pivoted at said third axis, and wherein said machinesfurther comprises a second crank means operatively engaging said supportmeans and rotatable about a fourth axis, said drive means rotating bothsaid first and second crank means at the same speed.
 20. The machineaccording to claim 19 wherein the distance between said fourth axis andsaid first axis is greater than the distance between said first axis andsaid machining line.
 21. The machine according to claim 1 wherein saidtool is a cylindrical grinding wheel having a tool axis parallel to saidmachine line.
 22. The machine according to claim 21 further comprisingwheel dressing means movable relative to said grinding wheel fordressing the surface thereof, said dressing means being positioned tocontact the cutting surface of said grinding wheel along a predetermineddressing line which is substantially parallel to said tool axis.
 23. Themachine according to claim 22 wherein said dressing line is coincidentwith said machining line.
 24. The machine according to claim 23 whereinthe distance between said dressing line and said crank axis is less thanthe distance between said crank axis and said machining line.
 25. Themachine according to claim 12 further comprising means for moving saidtool axis along said imaginary plane relative to said machining line.26. The machine according to claim 19 comprising further means carriedby said support means for moving said tool axis relative to saidmachining line along said imaginary plane.
 27. Th machinE according toclaim 12 wherein said drive means rotates said crank means about saidfirst axis in a first direction while rotating said work-holding meansabout the second axis in the opposite direction.